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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Bayesian analysis for nonlinear regression model under skewed errors, with application in growth curves.

Rolando De la Cruz1, Márcia D Branco

  • 1Departamento de Salud Pública, Escuela de Medicina, Pontificia Universidad Católica de Chile, Santiago, Chile. rolando@med.puc.cl

Biometrical Journal. Biometrische Zeitschrift
|July 25, 2009
PubMed
Summary

This study introduces a Bayesian nonlinear regression model using skewed distributions for error terms, accounting for repeated, serially correlated measurements. The skew-t model best fit growth curve data from pregnant women, outperforming standard models.

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Nonlinear regression models often assume normally distributed errors, which may not capture complex data patterns.
  • Repeated measurements within individuals frequently exhibit serial correlation and non-normal error distributions (skewness, heavy tails).
  • Accurate modeling of growth curves is crucial in clinical and epidemiological studies.

Purpose of the Study:

  • To develop and apply a Bayesian nonlinear regression framework accommodating skewed error distributions and serial correlation.
  • To compare model performance using various criteria, including the deviance information criterion (DIC), conditional predictive ordinate (CPO), and proper scoring rules.
  • To identify the most suitable error distribution for modeling longitudinal growth data.

Main Methods:

  • Bayesian nonlinear regression with skewed error distributions (e.g., skew-t).
  • Incorporation of serial correlation structures for repeated measures.
  • Parameter estimation and prediction via Markov Chain Monte Carlo (MCMC) simulation.
  • Model comparison using DIC, CPO, and posterior predictive scoring rules.

Main Results:

  • The skew-t error distribution model demonstrated superior fit for the growth curve data of pregnant women.
  • Model comparison criteria, including scoring rules, favored the skew-t model.
  • A simulation study validated the performance of DIC and CPO for the proposed models.

Conclusions:

  • The Bayesian approach with skewed error distributions effectively models longitudinal data with serial correlation.
  • The skew-t model is a robust choice for analyzing such complex biological or clinical data.
  • The deviance information criterion (DIC) may be unreliable for complex Bayesian models, necessitating the use of alternative criteria like proper scoring rules.